To write the equation of a parabola, we need some additional information, such as its vertex, direction (opened upward or downward), and any other specific points it may pass through.
Given the hint that the leading coefficient is \( \frac{1}{2} \), we can start by using the standard form of a parabola's equation. The general form of a parabola that opens upward or downward is:
\[ f(x) = a(x - h)^2 + k \]
where \((h, k)\) is the vertex and \(a\) is the leading coefficient.
Since the leading coefficient is specified as \( \frac{1}{2} \), we can rewrite our equation as:
\[ f(x) = \frac{1}{2}(x - h)^2 + k \]
Without further information about the vertex or specific points, we cannot fully define \(h\) and \(k\). If you have additional details regarding the vertex or specific points it passes through, I can help you complete the equation. Please provide that information!
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